Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe

Abstract

We reconstruct the expansion history of the universe using type Ia supernovae (SN Ia) in a manner independent of any cosmological model assumptions. To do so, we implement a nonparametric iterative smoothing method on the Joint Light-curve Analysis (JLA) data while exploring the SN Ia light-curve hyperparameter space by Markov Chain Monte Carlo (MCMC) sampling. We test to see how the posteriors of these hyperparameters depend on cosmology, whether using different dark energy models or reconstructions shift these posteriors. Our constraints on the SN Ia light-curve hyperparameters from our model-independent analysis are very consistent with the constraints from using different parameterizations of the equation of state of dark energy, namely the flat ΛCDM cosmology, the Chevallier–Polarski–Linder model, and the Phenomenologically Emergent Dark Energy (PEDE) model. This implies that the distance moduli constructed from the JLA data are mostly independent of the cosmological models. We also studied that the possibility the light-curve parameters evolve with redshift and our results show consistency with no evolution. The reconstructed expansion history of the universe and dark energy properties also seem to be in good agreement with the expectations of the standard ΛCDM model. However, our results also indicate that the data still allow for considerable flexibility in the expansion history of the universe.

Hints for possible low redshift oscillation around the best fit $Λ$CDM model in the expansion history of the Universe

“…• Making some internal consistency checks such as using "Robustness" criterion [85] or/and looking for redshift evolution in the light curve parameters of the data [86] to determine whether the Pantheon sample is statistically consistent or is contaminated with systematics.…”

Model selection and parameter estimation using the iterative smoothing method

“…The iterative smoothing method has been used so far mainly to reconstruct a non-exhaustive sample of viable expansion history possibilities that can fit the data with a better likelihood than a specific threshold. For instance, in L'Huillier et al ( 2018); Shafieloo et al (2018); Koo et al (2020) this method has been used to present a large sample of possibilities with viable smooth characteristics than can fit the data better than the best flat ΛCDM model. In this work, we attempt to tackle a different problem and seek to test the consistency of a particular model with the data by calculating a quantity we call the likelihood distribution, which is based on our reconstruction method and follows a frequentist statistical approach.…”

On The Distribution of Bayesian Evidences

“…The datasets that we use for this calculation are mock future supernova (SN) datasets as might be expected from the WFIRST telescope [8,30] and future baryon acoustic oscillation (BAO) datasets as might be expected from DESI [6,7] Type Ia SN are one of the observational pillars that built the ΛCDM model and directly measure the acceleration of the Universe. Existing SN datasets have all shown broad consistency with the ΛCDM model despite concerted searches for new physics or systematics [2,3,9,14,15,18,19,23,25,26,29,31]. These successes of SN exist because they are standardizable candles; the measurement and fitting of the light-curve of the SN allows us to infer the luminosity of the SN (up to a global calibration) [2,3,9,18,23,25,26,29,31], and thus measuring the flux is equivalent to measuring a luminosity distance, or equivalently a distance moduli:…”